In a military context, defending an area from an enemy offensive requires careful pre-processing in order to best assign the resources that are available to handle the threats, whilst maximising the survival expectancy of the strategic points that are defended.
Depending on the threats, a command and control system determines an engagement solution by taking into account operational and technical criteria.
Determining an engagement solution is not only based on assigning the available weapons to the targets, but is also based on selecting the firing time. The firing time can prove to be very complicated when faced with the numerous constraints and uncertainties that exist in such a complex system.
Therefore, modelling such a scenario poses a real problem that is encountered in the weapons industry when developing solutions to respond to this problem. Indeed, a solution must be able to be found that is based on a time horizon, but that is also able to model the areas of uncertainty when the threat is within range. An operator has to confirm an engagement based on the relevance of the proposed firing times, whilst taking into account the relevance of the associated probabilities of success. The engagement solution has to be feasible and optimal in terms of the probability of success.
A first conventional approach involves modelling the situation as a succession of weapon-to-target assignment problems in a static version. A danger level is assigned to each threat and each weapon is assigned a probability of success against this threat. The problem is rendered dynamic by considering a scenario on a step-by-step basis and by observing the outcomes of each of the combats resulting from the assignment undertaken during the preceding step.
A further conventional approach involves using a discrete time space and associating a probability of success therewith. This approach allows an engagement solution to be planned with a time horizon that is divided into sections. However, none of these solutions is satisfactory for the contemplated applications.
Indeed:                modelling the dynamic problem as a succession of static problems is not always enough for overcoming the real problem insofar as it does not take into account the continuity of the time and the long-term forecasting possibilities of an engagement solution. As the problem is reduced to a succession of static problems, the forecasting notion is absorbed. Long-term planning is not possible. This method does not allow firing to be sequenced for the overall optimisation of the problem; and        discrete time probability modelling does not allow the boundaries of the time segmentation to be reliably managed. Indeed, such modelling assumes that, between two very close time instants, the probability of success can change from 0 to a high value. This represents a significant modelling fault: for example, for the aforementioned application in the military field over ranges of several kilometres, a few metres is negligible and should not lead to such a significant difference.        
Consequently, a device or technical means do not exist that allow a resource allocation plan to be determined and optimised.